/*
 * @lc app=leetcode.cn id=37 lang=cpp
 *
 * [37] 解数独
 *
 * https://leetcode.cn/problems/sudoku-solver/description/
 *
 * algorithms
 * Hard (67.62%)
 * Likes:    1797
 * Dislikes: 0
 * Total Accepted:    236.9K
 * Total Submissions: 350.2K
 * Testcase Example:  '[["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]]'
 *
 * 编写一个程序，通过填充空格来解决数独问题。
 * 
 * 数独的解法需 遵循如下规则：
 * 
 * 
 * 数字 1-9 在每一行只能出现一次。
 * 数字 1-9 在每一列只能出现一次。
 * 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。（请参考示例图）
 * 
 * 
 * 数独部分空格内已填入了数字，空白格用 '.' 表示。
 * 
 * 
 * 
 * 
 * 
 * 
 * 示例 1：
 * 
 * 
 * 输入：board =
 * [["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]]
 * 
 * 输出：[["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","5","2","8","6","1","7","9"]]
 * 解释：输入的数独如上图所示，唯一有效的解决方案如下所示：
 * 
 * 
 * 
 * 
 * 
 * 
 * 提示：
 * 
 * 
 * board.length == 9
 * board[i].length == 9
 * board[i][j] 是一位数字或者 '.'
 * 题目数据 保证 输入数独仅有一个解
 * 
 * 
 * 
 * 
 * 
 */

// @lc code=start
class Solution {
public:
    bool IsValid(const vector<vector<char>>& board, int i, int j, char k) {
        int row = i / 3 * 3, col = j / 3 * 3;

        //列
        for (int r = 0; r < 9; r++)
            if (board[r][j] == k)
                return false;

        //行
        for (int c = 0; c < 9; c++)
            if (board[i][c] == k)
                return false;

        //九宫格
        for (int r = row; r < row + 3; r++)
            for (int c = col; c < col + 3; c++)
                if (board[r][c] == k)
                    return false;

        return true;
    }

    bool BackTracking(vector<vector<char>>& board) {
        for (int i = 0; i < 9; i ++) {
            for (int j = 0; j < 9; j++) {
                if (board[i][j] != '.')
                    continue;

                for (int k = 0; k < 9; k++) {
                    if (IsValid(board, i, j, '1' + k)) {
                        board[i][j] = '1' + k;
                        if (BackTracking(board))    //找到结果直接返回
                            return true;

                        //不用在意 false 的情况, 表示后面的不能满足要求
                        //需要更改当前格子的数字进行回溯

                        board[i][j] = '.';
                    }

                }

                //连续试了 9 个数, 发现没有结果, 直接返回 false
                //上层得知不是 true, 则会进行回溯
                return false;
            }
        }

        return true;    //遍历完全, 找到棋盘, 不再回溯
    }

    void solveSudoku(vector<vector<char>>& board) {
        //有且只有一个解, 得到结果后直接返回

        BackTracking(board);
    }
};
// @lc code=end

